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Numerische Mathematik

, Volume 140, Issue 1, pp 239–264 | Cite as

A fast sparse grid based space–time boundary element method for the nonstationary heat equation

  • Helmut Harbrecht
  • Johannes Tausch
Article

Abstract

This article presents a fast sparse grid based space–time boundary element method for the solution of the nonstationary heat equation. We make an indirect ansatz based on the thermal single layer potential which yields a first kind integral equation. This integral equation is discretized by Galerkin’s method with respect to the sparse tensor product of the spatial and temporal ansatz spaces. By employing the \(\mathcal {H}\)-matrix and Toeplitz structure of the resulting discretized operators, we arrive at an algorithm which computes the approximate solution in a complexity that essentially corresponds to that of the spatial discretization. Nevertheless, the convergence rate is nearly the same as in case of a traditional discretization in full tensor product spaces.

Mathematics Subject Classification

35K20 65F50 65M38 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departement Mathematik und InformatikUniversität BaselBaselSwitzerland
  2. 2.Department of MathematicsSouthern Methodist UniversityDallasUSA

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